Turbo codes and LPPC codes represent the leading edge of contemporary channel coding theory and practice. As a hybrid of turbo and LDPC codes, accumulator-based irregular LDPC codes (IRA) with quasi-cyclic structure have been widely adopted in communication standards including IEEE 802.11n, IEEE 802.16e and ETSI's second generation standards for digital video broadcasting (DVB). The IRA codes control their degree-2 variable nodes in a distinctive way to ensure a linear coding complexity, a low error floor as well as the stability of iterative decoding.
On the other hand, coding theorists and practitioners have recognized that a well-designed LDPC code can achieve capacity-approaching performance universally across a range of data transmission and storage channels. One example is ETSI's second generation DVB standards, which reuse the same LDPC codes for satellite, terrestrial and cable communication. Although this is not an optimal way to achieve capacity like the multi-level codes and the single channel code tailored to a given modulation format, it preserves the compatibility of CODEC structure and avoids the prohibiting complexity of implementation. The DVB LDPC codes family (with two block length 16200 and 64800; code rates coverage from 1/4 to 9/10) was originally developed for satellite communications (DVB-S2), which targeted modulations including BPSK, QPSK, 8PSK, 16APSK and 32APSK. These LDPC codes belong to the class of structured irregular repeat accumulate (S-IRA) codes. As demonstrated by prior methods, the structural simplicity can be admitted to the code ensemble to facilitate a linear complexity for encoding and decoding, without compromising the performance in both waterfall and error floor regions. In particular, under non-iterative modulation and conventional sum-product decoding, the DVB-S2 codes have been shown to be only 0.7-0.8 dB away from Shannon capacity limit at a bit error rate of 10−6. As a consequence, they have been adopted by standardization bodies for terrestrial and cable communications, and will be reused over terrestrial and cable channels. Nevertheless, the spectral efficiency of each channel type is distinct and needs to be considered in the joint design for coding and modulation. For example, DVB-T2 supports QAM order as high as 256, and DVB-C2 will make 4096-QAM mandatory to meet the demand for higher data rates. In order to preserve the low complexity of channel CODEC and achieve a power-efficient constellation mapping, a random bit interleaver can be plugged between the channel encoder and the constellation mapper to match the irregular profile of a given code to the non-uniform error resilience of a multi-level modulation. This paradigm is generally known as bit-interleaved coded modulation (BICM). Although the insertion of a random bit interleaver typically yields good performance, it is problematic for high-speed implementation for coding and modulation due to the substantial amount of memory and circuits routing involved.
Some work has previously been done in studying the framework of code design for a volume holographic memory (VHM) system with non-uniform error correction requirements. Actually, the model of non-uniform parallel channels can be extended to other applications, such as multi-level modulation, OFDM systems and punctured codes. Moreover, both theoretical analysis and simulation results have demonstrated that the decoding threshold does not depend appreciably on the channel details, but on the mutual information between the input and the output of the effective channel.